Question

The curved surface of a solid metallic sphere is cut in such a way that the curved surface area of the new sphere is half of that previous one . Let us calculate the ratio of the volumes of the portion cut off and the remaining portion of the sphere.​

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

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Let the radius of the old sphere be =R unit

let the radius of the new sphere be =r unit

therefore,curved surface area of the old sphere =4πR²

and the curved surface area of the new sphere =4πr²

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ATP,

4πR²/2=4πr²

or,R²=2r²

or ,R²=√2r²

or,R²=√2r

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now,volume of the old sphere=4/3πr³=4/3(2r)³ cubic unit

volume of the new sphere=4/3πr³

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volume of the remaining sphere =4/3(√2 r)³-4/3 πr³

⠀⠀ ⠀⠀ ⠀ ⠀⠀ ⠀⠀ ⠀⠀ ⠀⠀ ⠀ =4/3π³(2√2-1)

therefore,the ratio of the cut off portion and remaining part =4/3πr³:4/3πr³(2√2-1)

=1:2√2-1 (ANS)

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hope this helps you.